I don't believe in infinity.
Do you believe space is finite, or cyclical?
I'm not sure the two are mutually exclusive. I believe there's a finite amount of matter, therefore, a finite space to house it.
I think the ability to comprehend infinity is a function of the way our brains work, rather than a description of the way things really are. If you accept the idea of the infinite divisibility of space, for example, you run into a paradox (you can't ever move from point A to point B because first you have to go 1/2 of the way to B, but before that you have to go 1/4 of the distance to B, and so on). Reality doesn't work that way. If you assume infinity is just a concept rather than a description of the way things are the paradox goes away.